# Solving a multivariate polynomial system takes too long

I have tried to solve this system

``````Solve(2 w2 x2 + 2 w3 x3 - y1 - 4 w2^2 y1 - 4 w3^2 y1 + 2 w2 y2 + 2 w3 y3 +
4 w1 (w2 (x2 + y2) + w3 (1 + x3 + y3)) + 2 x2 z1 + 2 y2 z1 -
4 y1 z2 + 4 x2 z1 z2 + 4 y2 z1 z2 - 4 y1 z2^2 + 4 z1 z3 +
4 x3 z1 z3 + 4 y3 z1 z3 - 4 y1 z3^2 -
x1 (3 + 4 w2^2 + 4 w3^2 + 4 z2 + 4 z2^2 + 4 z3^2) == 0 && x2 y1 + y1 y2 - 4 z1 - 8 w2^2 z1 - 8 w3^2 z1 - 2 x2^2 z1 - 4 x3 z1 -
2 x3^2 z1 - 4 x2 y2 z1 - 2 y2^2 z1 - 4 y3 z1 - 4 x3 y3 z1 -
2 y3^2 z1 + 4 w2 z2 + 2 x2 y1 z2 + 2 y1 y2 z2 + 4 w3 z3 + 2 y1 z3 +
2 x3 y1 z3 + 2 y1 y3 z3 + 4 w1 (w2 + 2 w2 z2 + 2 w3 z3) +
x1 (x2 + y2 + 2 x2 z2 + 2 y2 z2 + 2 (1 + x3 + y3) z3) == 0 && -2 w2 x1 x2 + x2^2 + x3 + x3^2 - 2 w2 x2 y1 - 2 w2 x1 y2 + 2 x2 y2 -
2 w2 y1 y2 + y2^2 + y3 + 2 x3 y3 + y3^2 - 4 w2 z1 + 2 z2 -
8 w2 z1 z2 + 4 z2^2 + 4 z3^2 -
2 w3 (x1 (1 + x3 + y3) + y1 (1 + x3 + y3) + 4 z1 z3) +
2 w1 (3 + x2^2 + x3^2 + 2 x2 y2 + y2^2 + 2 y3 + y3^2 +
2 x3 (1 + y3) + 4 z2 + 4 z2^2 + 4 z3^2) == 0,
{x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3},Reals)
``````

but there is no output after a lot of hours, even days; Mathematica just says “running”. I do not have experience with Mathematica but I think that my code is correct (I want the solutions of this system for the real variables {x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3}). Can anybody help me? Is there something wrong with my code? I think that the only possible solution is x1=y1=z1=w1=x2=…=w3=0.